is it possible to find the value of cos theta equal to x square minus y square divided by X square + y square
Answers
Answer
we know that
sinθ=
hypotenuse
sideoppositetoangleθ
orsinθ=
hypotenuse
Perpendicular
sinθ=
x
2
+y
2
x
2
−y
2
⇒
H
P
=
x
2
+y
2
x
2
−y
2
⇒
BC
AB
=
x
2
+y
2
x
2
−y
2
side opposite to angle θ=AB=x
2
−y
2
hypotenuse AC=x
2
+y
2
In right angled △ABC, we have
⇒(AB)
2
+(BC)
2
=(AC)
2
⇒(x
2
−y
2
)
2
+(BC)
2
=(x
2
+y
2
)
2
⇒(BC)
2
=(x
2
+y
2
)
2
−(x
2
−y
2
)
2
(By Pythagoras theorem)
⇒(BC)
2
=[x
2
+y
2
+x
2
−y
2
][x
2
+y
2
−(x
2
−y
2
)]=(2x
2
)(2y
2
)
(using identity a
2
−b
2
=(a+b)(a−b))
BC=
4x
2
y
2
=±2xy
taking positie square root since, side cannot be negative
cosθ=
hypotenuse
Base
=
AC
BC
=
x
2
+y
2
2xy
and tanθ=
Base
Perpendicular
=
BC
AB
=
2xy
x
2
−y
2
so,
tanθ
1
=
2xy
x
2
−y
2
1
=
x
2
−y
2
2xy
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Answer:
The answer is 2xy
Step-by-step explanation:
these is common answer
ok